\(\sqrt{48-10\sqrt{7+4\sqrt 3}}\\=\sqrt{48-10\sqrt{4+4\sqrt 3+3}}=\sqrt{48-10\sqrt{(2+\sqrt 3)^2}}\\=\sqrt{48-10(2+\sqrt 3)}\\=\sqrt{48-20-10\sqrt 3}\\=\sqrt{28-10\sqrt 3}\\=\sqrt{25-10\sqrt 3+3}\\=\sqrt{(5-\sqrt 3)^2}\\=5-\sqrt 3\\→\sqrt{5\sqrt 3+5\sqrt{48-10\sqrt{7+4\sqrt 3}}}=\sqrt{5\sqrt 3+5(5-\sqrt 3)}\\=\sqrt{5(\sqrt 3+5-\sqrt 3)}\\=\sqrt{5.5}\\=\sqrt{25}=5\)